How fluent do I need to be in JavaScript before taking a crack at Unity's tutorials?

Like a little, a bit, very, or extremely?

Since Javascript (used in HTML pages) and Javascript (also named UnityScript) have nothing to do with each other (except maybe part of the syntax which are in both cases ECMA-compliant), I would say NONE.

You will learn more (and quicker) by experimenting and doing tutorials, than just playing around with the language.

If you don’t know any programming language at all, then the link provided @shawnkilian is a good start.

If you know at least one other programming language, you really can just dive in head first with making a few demo applications. Here is a scripting tutorial from Unity:

Hi, I just wanted to give my perspective. I came from flash so had some programming experience. I found the Unity tutorials to be very vague, they guide you through adding components, then edit some of their pre-written scripts, it was all very confusing. It was only when I started a WalkerBoys tutorial and wrote a project from nothing, did I finally understand how Unity worked. My suggestion is to follow the web links (provided below), as these cover both components and scripting quite well. As Bunny said, it depends on individual aptitude as to how quickly one can pick up uJS (or C#). Anyway, the best way to learn is to jump straight in, and practice practice practice =]

Start at the bottom and work up : Unity 3D Student - 3d Modelling

Start at the bottom and work up : Unity 3D Student - 3d Modelling

the Unity Wiki :

A list of resources : How can I start learning Unity fast? ( List Of Tutorials ) - Unity Answers